The sound you heard when Chris Columbus decided to step down as director of the “Harry Potter” movies was the cinephile quadrant of J. K. Rowling’s fan base letting out an exuberant squeal of joy. The first two installments of the “Harry Potter” series, helmed by Columbus, were so terribly, excruciatingly faithful to the source material that watching the movies was like having the books read to you by Abraham Simpson: they were long winded, with all of the emphasis placed on the unimportant details, and ultimately rather dull.

Not so, this one. Director Alfonso Cuarón (“Y Tu Mama Tambien”) adds a healthy dose of mean to the mix, and what a difference it makes. “Harry Potter and the Prisoner of Azkaban” is not only a better story than the previous installment, “Harry Potter and the Chamber of Secrets” (admittedly not a tough task), but it is considerably more entertaining to simply watch, and it’s almost entirely because of that added dose of menace that Cuarón and screenwriter Steve Kloves inject into the story. Growing up is hard enough for us Muggles; it certainly can’t be any easier for wizards and witches. This is the first “Potter” movie that examines this.

From nearly the very first scene, Potter (Daniel Radcliffe) shows the havoc that adolescence can wreak, when his short temper gets the best of him and he takes it out on his awful Aunt Marge (the condition he inflicts upon her is most apt.) Unfortunately, Hogwart’s isn’t exactly a refuge, either: A convict named Sirius Black (Gary Oldman) has just escaped from Azkaban prison, the first to ever do so. Harry learns that it was Black who sold out Harry’s parents and sent them to their deaths many years earlier. The Black sightings around Hogwart’s convince all concerned that he’s come back to finish the rest of the family off, but first he’ll have to sneak past the soul-sucking Dementors, the Azkaban prison guards that now surround the school and are eager to recapture their prisoner.

This isn’t all there is to the story, of course, and that is where one of the problems lies with “Azkaban.” For as much streamlining as they did with the story (they omitted an entire subplot regarding a nosy journalist), the movie still clocks in at a timely 142 minutes. And yet, despite the considerable length, every character besides Harry, Hermione (Emma Watson) and Ron (Rupert Grint) -- even a new one like Emma Thompson’s daffy divination professor Trelawney -- makes little more than a cameo appearance. Professor Snape (Alan Rickman), in particular, is tragically underused.

The new Defense Against the Dark Arts teacher Lupin (David Thewlis), however, does not receive short shrift, which should tell you something. What they don’t explain, though, is why Potter nemesis Draco Malfoy (Tom Felton, clearly experiencing a growth spurt) has become a sniveling sissy who seems to be afraid of his own shadow. Also, Michael Gambon, replacing the late Richard Harris, plays headmaster Dumbledore without any of the warmth that Harris brought to the character. It’s the one instance where adding some meanness doesn’t work. It is unclear whether that was their intention, but that’s what happened nonetheless.

However, for the few things that are a little off, they got some details just right; the Whomping Willow, for example, dispenses its justice on all God’s creatures, and it’s actually an amusing thing to behold. The Quidditch scene is mercifully short. And we’re starting to see signs of our three wizards, um, discovering each other, all of which point toward the next installment, “Harry Potter and the Goblet of Fire,” becoming the best of the bunch. But, with a length 300 pages longer than “Azkaban,” the screenwriters have their work cut out for them. Still, this neither is the time nor the place to diminish the significance of what Warners has done with the Harry Potter franchise: they actually made a third installment that bests its predecessors. A rare achievement, if ever there was one.